Type: Article
Publication Date: 2021-02-15
Citations: 5
DOI: https://doi.org/10.1155/2021/6624509
The split feasibility problem <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>SFP</mtext> </mrow> </mfenced> </math> has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>C</mi> <mi>Q</mi> </math> algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.